Question

If $\frac{0.0048}{x^2}=3$, find the value of $x(\ne 0)$.

• A. $0.0016$
• B. $0.016$
• C. $0.04$
• D. $0.4$

Answer 1

The correct option is C $0.04$

$\underset{–}{\text{Need to find:}}$ Value of $x$ for which $\frac{0.0048}{x^2}=3$

As $x\ne 0$, multiplying both sides of the equation by $x^2$.

$\frac{0.0048}{x^2}=3$

$\Rightarrow \frac{0.0048}{x^2}\times x^2=3\times x^2$

$\Rightarrow 3x^2=0.0048$

By dividing both sides of the equation by $3$, we get:

$\Rightarrow \frac{3x^2}{3}=\frac{0.0048}{3}$

$\Rightarrow x^2=\frac{0.0048}{3}$

In $0.0048,$ if we put the decimal point after $48$ then we need to move the decimal point $4$ places to the right, and the corresponding exponent to the base $10$ would be $-4$.

$\Rightarrow x^2=\frac{48\times {10}^{-4}}{3}$

$\Rightarrow x^2=\frac{16\times 3\times {10}^{-4}}{3}$
$(\because 48=16\times 3)$

$\Rightarrow x^2=\frac{16}{{10}^4}(\because a^{-n}=\frac{1}{a^n})$

$\Rightarrow x^2=\frac{16}{10000}$

$\Rightarrow x^2=\frac{4^2}{{100}^2}$
$(\because 16=4\times 4=4^2,10000=100\times 100={100}^2)$

$\Rightarrow x^2=(\frac{4}{100}{)}^2[\because \frac{a^n}{b^n}=(\frac{a}{b}{)}^n]$

By taking the square root on both the sides, we get

$\Rightarrow \sqrt{x^2}=\sqrt{(\frac{4}{100}{)}^2}$

$\Rightarrow x^{2\times \frac{1}{2}}=(\frac{4}{100}{)}^{2\times \frac{1}{2}}$

$\Rightarrow x=\frac{4}{100}$

$\Rightarrow \underset{–}{x=0.04}$

Hence, the value of $x$ in the equation $\frac{0.0048}{x^2}=3$ is $0.04$.

$\therefore$ Option (c.) is the correct answer.